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dc.contributor.authorRobdera, Mangatiana A.
dc.contributor.authorKagiso, Dintle
dc.date.accessioned2014-10-06T13:01:22Z
dc.date.available2014-10-06T13:01:22Z
dc.date.issued2013-11
dc.identifier.citationRobdera, M.A. & Kagiso, D. (2013) On the differentiability of vector valued additive set functions, Advances in Pure Mathematics, No. 3, pp. 653-659en_US
dc.identifier.issn2160-2384
dc.identifier.urihttp://hdl.handle.net/10311/1276
dc.descriptionSymbols on the original document may not be the same as in this abstract.en_US
dc.description.abstractThe Lebesgue-Nikodým Theorem states that for a Lebesgue measure λ:Σ〖⊂2〗^Ω→[0,∞) an additive set function F:Σ→R which is λ-absolutely continuous is the integral of a Lebegsue integrable a measurable function f:Ω→R; that is, for all measurable sets A, F(A)=∫_A▒〖fdλ.〗 Such a property is not shared by vector valued set functions. We introduce a suitable definition of the integral that will extend the above property to the vector valued case in its full generality. We also discuss a further extension of the Fundamental Theorem of Calculus for additive set functions with values in an infinite dimensional normed space.en_US
dc.language.isoenen_US
dc.publisherScientific Research, http://www.scirp.orgen_US
dc.rightsAvailabe under Creative Common Attribution Licenseen_US
dc.subjectVector integralen_US
dc.subjectLebesgue theoremsen_US
dc.subjectFundamental theorems of calculusen_US
dc.titleOn the differentiability of vector valued additive set functionsen_US
dc.typePublished Articleen_US
dc.rights.holderRobdera, Mangatianaen_US
dc.linkhttp://www.scirp.org/journal/PaperInformation.aspx?paperID=40079en_US


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